Learn, remember and apply the following :
(a + b)(a + 2b) = a² + ab + 2ab + 2b²
= a² + 3ab + 2b²
↓ ↓ ↓
first middle last
term term term
NOTE
* The first term is the product of the
first terms, i.e. a² = a x a
* The middle term is the algebraic
sum of the product of the
outer terms [ a x 2b ]
and the product of the
inner terms [ a x b ],
i.e. 3ab = [2a x b] + [a x b] = 2ab + ab
* The last term is the product of the
second terms, i.e. 2b2 = b x 2b
(p + 2)(3p + 5) = (p x 3p) + [(p x 5) + (2 x 3p)] + (2 x 5)
= 3p2 + 11p + 10